An isolated system consists of a 1.5 kg mass moving in the presence of the following potential energy function: U open parenthes
es x close parentheses equals open parentheses 1 third straight J over straight m cubed close parentheses x cubed plus open parentheses 1 half straight J over straight m squared close parentheses x squared minus open parentheses 2 straight J over straight m close parentheses x What is the period (in s) of small amplitude oscillations of this system about its stable equilibrium point?
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Answer:
The final components of velocity of the composite object is 3.33 m/s.
Explanation:
Given;
mass of the first object, m₁ = 3.35 kg
initial velocity of the first object, u₁ = 4.90 m/s in positive x-direction
mass of the second object, m₂ = 1.88 kg
initial velocity of the second object, u₂ = 3.12 m/s in negative y-direction
initial momentum of the first object, P₁ = 3.35 x 4.9 = 16.415 kgm/s
initial momentum of the second object, P₂ = 1.88 x 3.12 = 5.8656 kgm/s
The resultant velocity of the two objects is given by;
R² = 16.415² + 5.8656²
R² = 303.858
R = √303.858
R = 17.432 kgm/s
Apply the principle of conservation of linear momentum for inelastic collision;
total initial momentum before = total final momentum after collision
P₁(x) + P₂(y) = Pf
R = Pf
R = v(m₁ + m₂)
17.432 = v(m₁ + m₂)
where;
v is the final components of velocity of the composite object
Therefore, the final components of velocity of the composite object is 3.33 m/s.